Related papers: Normalization for Implied Volatility
We develop a dynamic version of the SSVI parameterisation for the total implied variance, ensuring that European vanilla option prices are martingales, hence preventing the occurrence of arbitrage, both static and dynamic. Insisting on the…
After a brief review of option pricing theory, we introduce various methods proposed for extracting the statistical information implicit in options prices. We discuss the advantages and drawbacks of each method, the interpretation of their…
In previous works Avellaneda et al. pioneered the pricing and hedging of index options - products highly sensitive to implied volatility and correlation assumptions - with large deviations methods, assuming local volatility dynamics for all…
Within a financial model with linear price impact, we study the problem of hedging a covered European option under gamma constraint. Using stochastic target and partial differential equation smoothing techniques, we prove that the…
Extracting implied information, like volatility and/or dividend, from observed option prices is a challenging task when dealing with American options, because of the computational costs needed to solve the corresponding mathematical problem…
Recent years have seen an emerging class of structured financial products based on options linked to dynamic asset allocation strategies. One of the most chosen approach is the so-called target volatility mechanism. It shifts between risky…
Several models for the pricing of derivative securities in illiquid markets are discussed. A typical type of nonlinear partial differential equations arising from these investigation is studied. The scaling properties of these equations are…
The variance gamma model is a widely popular model for option pricing in both academia and industry. In this paper, we provide a new perspective for pricing European style options for the variance gamma model by deriving closed-form…
We show that, for the purpose of pricing Swaptions, the Swap rate and the corresponding Forward rates can be considered lognormal under a single martingale measure. Swaptions can then be priced as options on a basket of lognormal assets and…
We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finite dimensional Gaussian process (GP)…
We study the fair strike of a discrete variance swap for a general time-homogeneous stochastic volatility model. In the special cases of Heston, Hull-White and Schobel-Zhu stochastic volatility models we give simple explicit expressions…
We present a deep learning framework for pricing options based on market-implied volatility surfaces. Using end-of-day S\&P 500 index options quotes from 2018-2023, we construct arbitrage-free volatility surfaces and generate training data…
One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets.…
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…
We propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler-Maruyama scheme. We study its…
Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the…
Market illiquidity, feedback effects, presence of transaction costs, risk from unprotected portfolio and other nonlinear effects in PDE based option pricing models can be described by solutions to the generalized Black-Scholes parabolic…
In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation…
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and…
We consider a non-Gaussian option pricing model, into which the underlying log-price is assumed to be driven by an $\alpha$-stable distribution. We remove the a priori divergence of the model by introducing a Mellin regularization for the…